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Density of the lexicographically ordered space $ \{0,1\}\sp \alpha$

Author: W. W. Comfort
Journal: Proc. Amer. Math. Soc. 109 (1990), 523-525
MSC: Primary 54A25; Secondary 54F05
MathSciNet review: 1000150
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Abstract: For an infinite cardinal $ \alpha $, the lexicographically ordered space $ {\left\{ {0,1} \right\}^\alpha }$ is denoted $ \Lambda (\alpha )$; its density is denoted $ d\Lambda (\alpha )$. Completing a computation left unfinished elsewhere, we prove $ d\Lambda (\alpha ) = {2^{_\smile ^\alpha }}$.

References [Enhancements On Off] (What's this?)

  • [1] W. W. Comfort and S. Negrepontis, The theory of ultrafilters, Grundlehren der Math. Wissenchaften, Band 211, Springer-Verlag, Berlin-Heidelberg-New York, 1974. MR 0396267 (53:135)
  • [2] W. W. Comfort and D. Remus, Long chains of Hausdorff topological group topologies,(submitted for publication).
  • [3] M. A. Maurice, Compact ordered spaces, Mathematical Centre Tracts, no. 6, Mathematisch Centrum, Amsterdam, 1964.
  • [4] W. Sierpiński, Sur une propriété des ensembles ordonnés, Fund. Math. 36 (1949), 56-67. MR 0031528 (11:165b)

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Keywords: Density, lexicographic order
Article copyright: © Copyright 1990 American Mathematical Society

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